The Condensed-Matter Sub-Programme

Electronic quantum matter from the non-injective projective substrate.

Overview

This sub-programme gathers the condensed-matter applications of the Cosmochrony framework. Both rest on the same object — the Weil–Heisenberg substrate $\mathrm{Heis}_3(\mathbb{Z}/q\mathbb{Z})$ and its winding sector $w=2$ — but read two complementary regimes of it.

In the superconductivity paper, the stabilisation and condensation of the $w=2$ composite is the pairing mechanism: superconductivity is projective phase locking of that composite, with $d$-wave symmetry in cuprates and extended $s^\pm$ symmetry in nickelates following from real-space frustration minimisation. In the quantum Fisher information note, the same substrate is read in its uncondensed, fluctuating regime: the scale-free growth of the quantum Fisher information density measured in a strange metal is a property of the full nilpotent substrate, not of any single composite.

Complementarity. A condensed $w=2$ composite carries superconductivity; the full, fluctuating and uncondensed substrate carries the scale-free multipartite entanglement of the strange metal. The two analyses are kept as separate notes for exactly this reason.

Constituent papers

Position within Cosmochrony

The sub-programme imports the substrate and the winding sector $w=2$ from the O-series spectral admissibility sub-programme, the Born–Infeld bounded-flux constraint from the foundational papers, and the heat-kernel identification of the diffusion scale with inverse temperature from the spectral thermodynamics paper. The quantum Fisher information note also defines a new spectral entanglement witness, complementary to the entanglement sub-programme: the projection entropy bounds Bell–CHSH violations and the residual-rank entropy counts conjugate-pair entanglement, whereas the quantum Fisher information counts the multipartite correlation depth of the steady state, which grows as the projective stability gap closes.

References

Beau, J. A Unified Real-Space Frustration Mechanism for Superconductivity. Preprint, 2026. https://doi.org/10.5281/zenodo.18718224

Beau, J. Quantum Fisher Information as a Spectral Entanglement Witness: the Projective Stability Gap and the Origin of Scale-Free Growth. Preprint, 2026. https://doi.org/10.5281/zenodo.21001565